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Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.


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TL;DR: In this article, the rate-problem of continuing equilibrium for a general class of rate-independent elastoplastic solids, without assuming the normality flow rule or symmetry of the tangent stiffness matrix, is examined.
Abstract: The rate-problem of continuing equilibrium is examined for a general class of rate-independent elastoplastic solids, without assuming the normality flow rule or symmetry of the tangent stiffness matrix. Accordingly, the problem addressed is of non-potential type, for which the usual stationarity or minimum principles for a governing potential do not apply. It is shown that the rate-problem can nevertheless be formulated as a quasi-extremal energy principle. It is characterized by explicit dependence of the minimized energy function or functional not only on variables undergoing variations but also, although only in a particular way, on an unknown solution as a parameter. To enable transparent and mathematically simple presentation of the main concept, the energy function is defined in a finite-dimensional setting for a spatially discretized material body with generalized velocities and a number of plastic multipliers as unknowns. If a solution is non-unique then incrementally stable solutions can be selected using the quasi-extremal principle in which the minimized energy function includes the second-order terms. Examples and extensions concern an elastic-plastic continuum obeying a non-associative plastic flow rule, without or with a higher-order gradient term in the loading function. The issue of selection of active slip-systems in a single crystal of a non-symmetric slip-system interaction matrix is also addressed.

14 citations

Journal ArticleDOI
TL;DR: In this paper, a complete and symmetric tangent stiffness matrix is obtained by considering up to the quadratic term of Taylor expansion of a finite rotation tensor for a 4-node shell element which includes the effect of large rotation increments.
Abstract: An efficient formulation for a 4-node shell element which includes the effect of large rotation increments is presented. The formulation is based on the MITC element proposed by Bathe et al. A complete and symmetric tangent stiffness matrix is obtained by considering up to the quadratic term of Taylor expansion of a finite rotation tensor. Several numerical examples are demonstrated to show the superior convergence by the present formulation compared with the conventional MITC formulation which assumes infinitesimal rotation increments. It is also shown in sensitivity analysis that accurate gradients are always obtained by the complete tangent stiffness, although erroneous gradients can be obtained by the conventional ones.

13 citations

Journal ArticleDOI
TL;DR: In this article, the nonintrusive local continuum shape sensitivity method with spatial gradient reconstruction (SGR) is formulated for nonlinear systems, which is an extension of the formulation previously published for linear systems.
Abstract: Gradient-based optimization for large-scale, multidisciplinary design problems requires accurate and efficient sensitivity analysis to compute design derivatives. Presented here is a nonintrusive analytic sensitivity method, that is relatively easy to implement. Furthermore, it can be as accurate as conventional analytic sensitivity methods, which are intrusive and tend to be difficult, if not infeasible, to implement. The nonintrusive local continuum shape sensitivity method with spatial gradient reconstruction (SGR) is formulated for nonlinear systems. This is an extension of the formulation previously published for linear systems. SGR, a numerical technique used to approximate spatial derivatives, can be leveraged to implement the sensitivity method in a nonintrusive manner. The method is used to compute design derivatives for a variety of applications, including nonlinear static beam bending, nonlinear transient gust response of a 2-D beam structure, and nonlinear static bending of rectangular plates. To demonstrate that the method is nonintrusive, all analyses are conducted using black box solvers. One limiting requirement of the method is that it requires the converged Jacobian or tangent stiffness matrix as output from the analysis tool. For each example the design derivatives of the structural displacement response are verified with finite difference calculations.

13 citations

Journal ArticleDOI
TL;DR: In this article, an integrated approach for all necessary variations within direct analysis, variational design sensitivity analysis and shakedown analysis based on Melan's static shakedown theorem for linear unlimited kinematic hardening material behavior is formulated.

13 citations

Journal ArticleDOI
TL;DR: In this article, a nonlocal discrete model is proposed to study the deformation and failure behaviors of cross-ply laminated composite plate under static or quasi-static mechanical loadings.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202241
202128
202016
201920
201829